Remarks on well-posedness theorems for damped second-order systems

AbstractWe consider an operator theoretic formulation for distributed damped second-order (in time) forced linear elastic systems. A brief summary of previous well-posedness results is presented along with new results which allow relaxed spatial regularity (which is important in smart material systems applications) on the forcing or input function. Extensions to nonlinear systems are also indicated. The results are presented in a variational format for easy development of finite element approximation methods

Projection series for retarded functional differential equations with applications to optimal control problems

AbstractIn this paper projection methods based on expansions of solutions of retarded function differential equations in terms of generalized eigenfunctions are considered. It is first shown that the projection series developed earlier by Hale and Shimanov and those considered by Bellman and Cooke are actually the same. Using extensions of the residue-type arguments of Bellman and Cooke, convergence results are then established for a class of perturbed systems. These results are applied to obtain approximations to optimal controls for certain infinite dimensional variational problems. Numerical results are presented for several examples

Estimation of nonlinearities in parabolic models for growth, predation, and dispersal of populations

AbstractA convergence theory is given for approximation techniques to treat inverse problems involving systems of nonlinear parabolic partial differential equations. These techniques can be used to estimate density-dependent dispersal coefficients in population models, as well as nonlinear growth and predation terms. Numerical experiences with the resulting algorithms on both conventional (scalar) and vector computers are reported along with an indication of performance of the methods with field data from prey-predator experiments

Pointwise convergence of approximation schemes for parameter estimation in parabolic equations

AbstractA finite element-based approximation scheme is presented for parameter estimation problems for parabolic PDEs on a two-dimensional domain. Pointwise convergence results relating the approximating subspaces to the full infinite-dimensional state space are discussed

Invariance in linear systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32794/1/0000167.pd

A dynamic model for induced reactivation of latent virus

We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms

Damage detections in nonlinear vibrating thermally loaded plates

In this work, geometrically nonlinear vibrations of fully clamped rectangular plates subjected to thermal changesare used to study the sensitivity of some vibration response parameters to the presence of damage and elevated temperature. The geometrically nonlinear version of the Mindlin plate theory is used to model the plate behaviour.Damage is represented as a stiffness reduction in a small area of the plate. The plates are subjected to harmonicloading leading to large amplitude vibrations and temperature changes. The plate vibration response is obtained by a pseudo-load mode superposition method. The main results are focussed on establishing the influence of damage on the vibration response of the heated and the unheated plates and the change in the time-history diagrams and the Poincaré maps caused by damage and elevated temperature. The damage criterion formulated earlier for nonheated plates, based on analyzing the points in the Poincaré sections of the damaged and healthy plate, is modified and tested for the case of plates additionally subjected to elevated temperatures. The importance of taking into account the actual temperature in the process of damage detection is shown

Greybody Factors for Rotating Black Holes on Codimension-2 Branes

We study the absorption probability and Hawking radiation of the scalar field in the rotating black holes on codimension-2 branes. We find that finite brane tension modifies the standard results in Hawking radiation if compared with the case when brane tension is completely negligible. We observe that the rotation of the black hole brings richer physics. Nonzero angular momentum triggers the super-radiance which becomes stronger when the angular momentum increases. We also find that rotations along different angles influence the result in absorption probability and Hawking radiation. Compared with the black hole rotating orthogonal to the brane, in the background that black hole spins on the brane, its angular momentum brings less super-radiance effect and the brane tension increases the range of frequency to accommodate super-radiance. These information can help us know more about the rotating codimension-2 black holes.Comment: 16 pages, 7 figures, minor modification, accepted for publication in JHE